model_fitting
load obs
obs_only <-
read_csv(glue("{params$model_dir_str}/data/stimulation_obvs.csv")) %>%
mutate(subj = as_factor(subj),
obs_degree = error,
error = obs_degree * (pi/180))## Parsed with column specification:
## cols(
## subj = col_double(),
## subj_index = col_double(),
## stimulation = col_double(),
## error = col_double()
## )# obs_only <- sim_data %>%
# unnest(subj_obs) %>%
# select(subj_index = subj,
# error = obs_radian,
# obs_degree,
# stimulation)peek at data
pre
obs_only %>%
filter(stimulation == 0) %>%
ggplot(aes(x = obs_degree)) +
geom_histogram(binwidth = 10, aes(y=..density..)) +
geom_rug() +
geom_density(aes(y=..density..)) +
facet_wrap(vars(subj), ncol = 1)
post
obs_only %>%
filter(stimulation == 1) %>%
ggplot(aes(x = obs_degree)) +
geom_histogram(binwidth = 10, aes(y=..density..)) +
geom_rug() +
geom_density(aes(y=..density..)) +
facet_wrap(vars(subj), ncol = 1)
fit brms
source(glue("{params$model_dir_str}/model_prior.R"))
print(bprior_full)## prior class coef group resp dpar nlpar bound
## 1 normal(3.8, 0.4) b intercept circSD
## 2 normal(0, 0.4) b stimulation circSD
## 3 normal(0, 0.25) sd Intercept subj circSD
## 4 normal(0, 0.25) sd stimulation subj circSD
## 5 normal(0, 1.5) b intercept theta
## 6 normal(0, 1) b stimulation theta
## 7 normal(0, 0.5) sd Intercept subj theta
## 8 normal(0, 0.5) sd stimulation subj thetaiter = 4000
warmup = 2000
cores = 4
chains = 4
n_post_samples = (iter - warmup) * chains
writeLines(
make_stancode(bform_full, obs_only, family = vm_uniform_mix, prior = bprior_full, stanvars = stanvars),
glue("{params$save_dir_str}/stan_code.txt")
)
model_fit <- brm(bform_full, obs_only, family = vm_uniform_mix, prior = bprior_full, stanvars = stanvars,
sample_prior = "yes",
warmup = warmup, iter = iter, cores = cores, chains = chains,
control = list(adapt_delta = 0.99), inits = 0,
file = glue("{params$save_dir_str}/obs_model_fit"))
print(model_fit)## Family: vm_uniform_mix
## Links: mu = identity; circSD = log; theta = logit; a = identity; b = identity
## Formula: error ~ 0
## circSD ~ 0 + intercept + stimulation + (1 + stimulation || subj)
## theta ~ 0 + intercept + stimulation + (1 + stimulation || subj)
## a = -3.14
## b = 3.14
## Data: obs_only (Number of observations: 504)
## Samples: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
## total post-warmup samples = 8000
##
## Group-Level Effects:
## ~subj (Number of levels: 2)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(circSD_Intercept) 0.21 0.14 0.01 0.54 1.00 3479
## sd(circSD_stimulation) 0.22 0.15 0.01 0.55 1.00 4366
## sd(theta_Intercept) 0.54 0.27 0.10 1.18 1.00 4560
## sd(theta_stimulation) 0.33 0.26 0.01 0.97 1.00 4779
## Tail_ESS
## sd(circSD_Intercept) 3271
## sd(circSD_stimulation) 2945
## sd(theta_Intercept) 2853
## sd(theta_stimulation) 3155
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## circSD_intercept 3.36 0.20 3.01 3.81 1.00 4739
## circSD_stimulation 0.24 0.23 -0.24 0.69 1.00 5548
## theta_intercept 0.13 0.45 -0.76 1.03 1.00 3444
## theta_stimulation -0.18 0.42 -1.00 0.67 1.00 5094
## Tail_ESS
## circSD_intercept 3873
## circSD_stimulation 4968
## theta_intercept 3829
## theta_stimulation 4900
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## b_circSD_intercept 3.36 0.20 3.01 3.81 1.00 4739
## b_circSD_stimulation 0.24 0.23 -0.24 0.69 1.00 5548
## b_theta_intercept 0.13 0.45 -0.76 1.03 1.00 3444
## b_theta_stimulation -0.18 0.42 -1.00 0.67 1.00 5094
## Tail_ESS
## b_circSD_intercept 3873
## b_circSD_stimulation 4968
## b_theta_intercept 3829
## b_theta_stimulation 4900
##
## Samples were drawn using sampling(NUTS). For each parameter, Eff.Sample
## is a crude measure of effective sample size, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).fit check
divergences
#check neff and rhat and divergences
np <- nuts_params(model_fit)
rhat <- brms::rhat(model_fit)
neff_rat <- neff_ratio(model_fit)
np %>%
filter(Parameter == "divergent__") %>%
summarise(n_div = sum(Value))## n_div
## 1 0rhat
mcmc_rhat(rhat) + yaxis_text(hjust = 1) + scale_x_continuous(breaks = pretty_breaks(6))## Scale for 'x' is already present. Adding another scale for 'x', which
## will replace the existing scale.
neff ratio
mcmc_neff(neff_rat) + yaxis_text(hjust = 1)
trace plots
mcmc_trace(as.array(model_fit$fit))
other
plot(model_fit, ask = FALSE)
* Notes
All looks good.
plot posteriors
arrange samples
# compute summaries for plot
group_level_samples <-
spread_draws(model_fit, `(b|sd)_.*`, regex = TRUE) %>%
mutate(
# group level parameters
circSD_pre_mean = exp(b_circSD_intercept),
circSD_post_mean = exp(b_circSD_intercept + b_circSD_stimulation),
circSD_ES_mean = circSD_post_mean - circSD_pre_mean,
pMem_pre_mean = inv_logit(b_theta_intercept),
pMem_post_mean = inv_logit(b_theta_intercept + b_theta_stimulation),
pMem_ES_mean = pMem_post_mean - pMem_pre_mean,
# predicitve dist for group level parameters
circSD_pre_pred = exp(rnorm(n(), b_circSD_intercept, sd_subj__circSD_Intercept)),
circSD_post_pred = exp(rnorm(n(), b_circSD_intercept, sd_subj__circSD_Intercept) +
rnorm(n(), b_circSD_stimulation, sd_subj__circSD_stimulation)),
circSD_ES_pred = circSD_post_pred - circSD_pre_pred,
pMem_pre_pred = inv_logit(rnorm(n(), b_theta_intercept, sd_subj__theta_Intercept)),
pMem_post_pred = inv_logit(rnorm(n(), b_theta_intercept, sd_subj__theta_Intercept) +
rnorm(n(), b_theta_stimulation, sd_subj__theta_stimulation)),
pMem_ES_pred = pMem_post_pred - pMem_pre_pred
) %>%
select(-contains("b_"), -contains("sd_subj")) %>%
pivot_longer(-contains("."), names_to = c("param", "stat"), names_pattern = "(.*)_(.*)", values_to = "value") %>%
pivot_wider(names_from = stat, values_from = value)
group_level_summary <-
group_level_samples %>%
group_by(param) %>%
median_qi(.width = c(.5, .8, .95))
circSD_subj_samples <-
model_fit %>%
spread_draws(b_circSD_intercept, b_circSD_stimulation, r_subj__circSD[subj, term]) %>%
ungroup() %>%
pivot_wider(names_from = term, values_from = r_subj__circSD, names_prefix = "offset_") %>%
mutate(subj = subj,
circSD_pre = exp(b_circSD_intercept + offset_Intercept),
circSD_post = exp(b_circSD_intercept + offset_Intercept + b_circSD_stimulation + offset_stimulation),
circSD_ES = circSD_post - circSD_pre) %>%
select(-c(b_circSD_intercept, offset_Intercept, b_circSD_stimulation, offset_stimulation)) %>%
pivot_longer(contains("circSD"), names_to = "param", values_to = "value")
circSD_subj_summary <-
circSD_subj_samples %>%
group_by(subj, param) %>%
median_qi(.width = c(.90, .95))## Warning: unnest() has a new interface. See ?unnest for details.
## Try `df %>% unnest(c(.lower, .upper))`, with `mutate()` if needed
## Warning: unnest() has a new interface. See ?unnest for details.
## Try `df %>% unnest(c(.lower, .upper))`, with `mutate()` if neededpMem_subj_samples <-
model_fit %>%
spread_draws(b_theta_intercept, b_theta_stimulation, r_subj__theta[subj, term]) %>%
ungroup() %>%
pivot_wider(names_from = term, values_from = r_subj__theta, names_prefix = "offset_") %>%
mutate(subj = subj,
pMem_pre = inv_logit(b_theta_intercept + offset_Intercept),
pMem_post = inv_logit(b_theta_intercept + offset_Intercept + b_theta_stimulation + offset_stimulation),
pMem_ES = pMem_post - pMem_pre) %>%
select(-c(b_theta_intercept, offset_Intercept, b_theta_stimulation, offset_stimulation)) %>%
pivot_longer(contains("pMem"), names_to = "param", values_to = "value")
pMem_subj_summary <-
pMem_subj_samples %>%
group_by(subj, param) %>%
median_qi(.width = c(.90, .95))## Warning: unnest() has a new interface. See ?unnest for details.
## Try `df %>% unnest(c(.lower, .upper))`, with `mutate()` if needed
## Warning: unnest() has a new interface. See ?unnest for details.
## Try `df %>% unnest(c(.lower, .upper))`, with `mutate()` if neededgroup_level_samples %>%
select(-pred) %>%
group_by(param) %>%
median_qi(.width = c(.95))## Warning: unnest() has a new interface. See ?unnest for details.
## Try `df %>% unnest(c(.lower, .upper))`, with `mutate()` if needed## # A tibble: 6 x 7
## param mean .lower .upper .width .point .interval
## <chr> <dbl> <dbl> <dbl> <dbl> <chr> <chr>
## 1 circSD_ES 8.10 -7.07 28.6 0.95 median qi
## 2 circSD_post 36.5 21.9 65.9 0.95 median qi
## 3 circSD_pre 28.5 20.3 45.0 0.95 median qi
## 4 pMem_ES -0.0436 -0.233 0.155 0.95 median qi
## 5 pMem_post 0.483 0.240 0.753 0.95 median qi
## 6 pMem_pre 0.530 0.319 0.738 0.95 median qigroup level posteriors
circSD_p1 <- group_level_samples %>%
filter(str_detect(param, "circSD")) %>%
ggplot() +
# posterior dist + interval for group mean
geom_halfeyeh(aes(y = param, x = mean), .width = c(.90, .95), position = position_nudge(y = 0.15)) +
# posterior predictive distribution for group means
stat_intervalh(aes(y = param, x = pred), .width = c(.5, .8, .95)) +
# posterior medians for each parameter estimate per subj
geom_point(data = circSD_subj_summary, aes(y = param, x = value), size = 2) +
# decorations
scale_color_brewer() +
scale_x_continuous(breaks = pretty_breaks(10)) +
coord_cartesian(xlim=c(-50, 150)) +
labs(subtitle = "circSD: group level mean posterior (median, 90%, 95% interval), \nsubject posterior medians, \ncondition predictive dist of subjects",
x = "circSD",
color = "interval")
# group level pMem pre, post and ES plot
pMem_p1 <- group_level_samples %>%
filter(str_detect(param, "pMem")) %>%
ggplot() +
# posterior dist + interval for group mean
geom_halfeyeh(aes(y = param, x = mean), .width = c(.90, .95), position = position_nudge(y = 0.15)) +
# posterior predictive distribution for group means
stat_intervalh(aes(y = param, x = pred), .width = c(.5, .8, .95)) +
# posterior medians for each parameter estimate per subj
geom_point(data = pMem_subj_summary, aes(y = param, x = value), size = 2) +
# decorations
scale_color_brewer() +
scale_x_continuous(breaks = pretty_breaks(10)) +
#coord_cartesian(xlim=c(-50, 150)) +
labs(subtitle = "pMem: group level mean posterior (median, 90%, 95% interval), \nsubject posterior medians, \ncondition predictive dist of subjects",
x = "pMem",
color = "interval")
plot_grid(circSD_p1, pMem_p1, align = "hv", ncol = 1)
circSD pre, post, ES
# circSD pre: group level posteriors and subject posteriors
circSD_p2 <-
ggplot() +
# plot group mean circSD_pre posterior and subject circSD_pre posterior
geom_halfeyeh(data = rbind(
group_level_samples %>%
filter(str_detect(param, "circSD_pre")) %>%
select(-pred, value = mean)
,
circSD_subj_samples %>%
filter(str_detect(param, "circSD_pre")) %>%
unite(param, param, subj) )
, aes(y = param, x = value), .width = c(.90, .95)) +
# plot pre condition group predictive distribution
stat_intervalh(data = group_level_samples %>% filter(str_detect(param, "circSD_pre")),
aes(y = param , x = pred),
.width = c(.5, .8, .95),
position = position_nudge(y = -0.15)
) +
# show modeled subject circSD_pre posterior medians in the prediction band
geom_point(data = circSD_subj_summary %>% filter(param == "circSD_pre"),
aes(y = param, x = value),
size = 2,
position = position_nudge(y = -0.15)) +
scale_color_brewer() +
scale_x_continuous(breaks = pretty_breaks(10)) +
labs(subtitle = "circSD_pre: group level mean posterior (median, 90%, 95% interval), \nsubject posterior, \ncondition predictive dist of subjects",
x = "circSD",
color = "interval")
circSD_p3 <-
ggplot() +
# plot group mean circSD_post posterior and subject circSD_post posterior
geom_halfeyeh(data = rbind(
group_level_samples %>%
filter(str_detect(param, "circSD_post")) %>%
select(-pred, value = mean)
,
circSD_subj_samples %>%
filter(str_detect(param, "circSD_post")) %>%
unite(param, param, subj) )
, aes(y = param, x = value), .width = c(.90, .95)) +
# plot post condition group predictive distribution
stat_intervalh(data = group_level_samples %>% filter(str_detect(param, "circSD_post")),
aes(y = param , x = pred),
.width = c(.5, .8, .95),
position = position_nudge(y = -0.15)
) +
# show modeled subject circSD_post posterior medians in the prediction band
geom_point(data = circSD_subj_summary %>% filter(param == "circSD_post"),
aes(y = param, x = value),
size = 2,
position = position_nudge(y = -0.15)) +
scale_color_brewer() +
scale_x_continuous(breaks = pretty_breaks(10)) +
labs(subtitle = "circSD_post: group level mean posterior (median, 90%, 95% interval), \nsubject posterior, \ncondition predictive dist of subjects",
x = "circSD",
color = "interval")
circSD_p4 <-
ggplot() +
# plot group mean circSD_ES posterior and subject circSD_ES posterior
geom_halfeyeh(data = rbind(
group_level_samples %>%
filter(str_detect(param, "circSD_ES")) %>%
select(-pred, value = mean)
,
circSD_subj_samples %>%
filter(str_detect(param, "circSD_ES")) %>%
unite(param, param, subj) )
, aes(y = param, x = value), .width = c(.90, .95)) +
# plot ES group predictive distribution
stat_intervalh(data = group_level_samples %>% filter(str_detect(param, "circSD_ES")),
aes(y = param , x = pred),
.width = c(.5, .8, .95),
position = position_nudge(y = -0.15)
) +
# show modeled subject circSD_ES posterior medians in the prediction band
geom_point(data = circSD_subj_summary %>% filter(param == "circSD_ES"),
aes(y = param, x = value),
size = 2,
position = position_nudge(y = -0.15)) +
scale_color_brewer() +
scale_x_continuous(breaks = pretty_breaks(10)) +
labs(subtitle = "circSD_ES: group level mean posterior (median, 90%, 95% interval), \nsubject posterior, \nES predictive dist of subjects",
x = "detla circSD",
color = "interval")
plot_grid(circSD_p2, circSD_p3, circSD_p4, ncol = 1, align = "hv")
pMem pre, post, ES
# pMem_ pre: group level posteriors and subject posteriors
pMem_p2 <-
ggplot() +
# plot group mean pMem__pre posterior and subject cpMem__pre posterior
geom_halfeyeh(data = rbind(
group_level_samples %>%
filter(str_detect(param, "pMem_pre")) %>%
select(-pred, value = mean)
,
pMem_subj_samples %>%
filter(str_detect(param, "pMem_pre")) %>%
unite(param, param, subj) )
, aes(y = param, x = value), .width = c(.90, .95)) +
# plot pre condition group predictive distribution
stat_intervalh(data = group_level_samples %>% filter(str_detect(param, "pMem_pre")),
aes(y = param , x = pred),
.width = c(.5, .8, .95),
position = position_nudge(y = -0.15)
) +
# show modeled subject pMem_pre posterior medians in the prediction band
geom_point(data = pMem_subj_summary %>% filter(param == "pMem_pre"),
aes(y = param, x = value),
size = 2,
position = position_nudge(y = -0.15)) +
scale_color_brewer() +
scale_x_continuous(breaks = pretty_breaks(10)) +
labs(subtitle = "pMem_pre: group level mean posterior (median, 90%, 95% interval), \nsubject posterior, \ncondition predictive dist of subjects",
x = "pMem",
color = "interval")
pMem_p3 <-
ggplot() +
# plot group mean pMem_post posterior and subject pMem_post posterior
geom_halfeyeh(data = rbind(
group_level_samples %>%
filter(str_detect(param, "pMem_post")) %>%
select(-pred, value = mean)
,
pMem_subj_samples %>%
filter(str_detect(param, "pMem_post")) %>%
unite(param, param, subj) )
, aes(y = param, x = value), .width = c(.90, .95)) +
# plot post condition group predictive distribution
stat_intervalh(data = group_level_samples %>% filter(str_detect(param, "pMem_post")),
aes(y = param , x = pred),
.width = c(.5, .8, .95),
position = position_nudge(y = -0.15)
) +
# show modeled subject pMem_post posterior medians in the prediction band
geom_point(data = pMem_subj_summary %>% filter(param == "pMem_post"),
aes(y = param, x = value),
size = 2,
position = position_nudge(y = -0.15)) +
scale_color_brewer() +
scale_x_continuous(breaks = pretty_breaks(10)) +
labs(subtitle = "pMem_post: group level mean posterior (median, 90%, 95% interval), \nsubject posterior, \ncondition predictive dist of subjects",
x = "pMem",
color = "interval")
pMem_p4 <-
ggplot() +
# plot group mean pMem_ES posterior and subject pMem_ES posterior
geom_halfeyeh(data = rbind(
group_level_samples %>%
filter(str_detect(param, "pMem_ES")) %>%
select(-pred, value = mean)
,
pMem_subj_samples %>%
filter(str_detect(param, "pMem_ES")) %>%
unite(param, param, subj) )
, aes(y = param, x = value), .width = c(.90, .95)) +
# plot ES group predictive distribution
stat_intervalh(data = group_level_samples %>% filter(str_detect(param, "pMem_ES")),
aes(y = param , x = pred),
.width = c(.5, .8, .95),
position = position_nudge(y = -0.15)
) +
# show modeled subject pMem_ES posterior medians in the prediction band
geom_point(data = pMem_subj_summary %>% filter(param == "pMem_ES"),
aes(y = param, x = value),
size = 2,
position = position_nudge(y = -0.15)) +
scale_color_brewer() +
scale_x_continuous(breaks = pretty_breaks(10)) +
labs(subtitle = "pMem_ES: group level mean posterior (median, 90%, 95% interval), \nsubject posterior, \nES predictive dist of subjects",
x = "detla pMem",
color = "interval")plot_grid(pMem_p2, pMem_p3, pMem_p4, ncol = 1, align = "hv")
group level joint posteriors
group_level_samples %>%
pivot_wider(id_cols = contains("."), names_from = param, values_from = mean) %>%
select(-contains(".")) %>%
mcmc_pairs(off_diag_fun = "hex")## Warning: Only one chain in 'x'. This plot is more useful with multiple
## chains.
plot posteriors w/ priors
# compute summaries for plot with priors
group_level_samples <-
spread_draws(model_fit, `(prior_)?(b|sd)_.*`, regex = TRUE) %>%
mutate(
# prior
# group level parameters
prior_circSD_pre_mean = exp(prior_b_circSD_intercept),
prior_circSD_post_mean = exp(prior_b_circSD_intercept + prior_b_circSD_stimulation),
prior_circSD_ES_mean = prior_circSD_post_mean - prior_circSD_pre_mean,
prior_pMem_pre_mean = inv_logit(prior_b_theta_intercept),
prior_pMem_post_mean = inv_logit(prior_b_theta_intercept + prior_b_theta_stimulation),
prior_pMem_ES_mean = prior_pMem_post_mean - prior_pMem_pre_mean,
# predicitve dist for group level parameters
prior_circSD_pre_pred = exp(rnorm(n(), prior_b_circSD_intercept, prior_sd_subj__circSD_Intercept)),
prior_circSD_post_pred = exp(rnorm(n(), prior_b_circSD_intercept, prior_sd_subj__circSD_Intercept) +
rnorm(n(), prior_b_circSD_stimulation, prior_sd_subj__circSD_stimulation)),
prior_circSD_ES_pred = prior_circSD_post_pred - prior_circSD_pre_pred,
prior_pMem_pre_pred = inv_logit(rnorm(n(), prior_b_theta_intercept, prior_sd_subj__theta_Intercept)),
prior_pMem_post_pred = inv_logit(rnorm(n(), prior_b_theta_intercept, prior_sd_subj__theta_Intercept) +
rnorm(n(), prior_b_theta_stimulation, prior_sd_subj__theta_stimulation)),
prior_pMem_ES_pred = prior_pMem_post_pred - prior_pMem_pre_pred,
# posteriors
# group level parameters
circSD_pre_mean = exp(b_circSD_intercept),
circSD_post_mean = exp(b_circSD_intercept + b_circSD_stimulation),
circSD_ES_mean = circSD_post_mean - circSD_pre_mean,
pMem_pre_mean = inv_logit(b_theta_intercept),
pMem_post_mean = inv_logit(b_theta_intercept + b_theta_stimulation),
pMem_ES_mean = pMem_post_mean - pMem_pre_mean,
# predicitve dist for group level parameters
circSD_pre_pred = exp(rnorm(n(), b_circSD_intercept, sd_subj__circSD_Intercept)),
circSD_post_pred = exp(rnorm(n(), b_circSD_intercept, sd_subj__circSD_Intercept) +
rnorm(n(), b_circSD_stimulation, sd_subj__circSD_stimulation)),
circSD_ES_pred = circSD_post_pred - circSD_pre_pred,
pMem_pre_pred = inv_logit(rnorm(n(), b_theta_intercept, sd_subj__theta_Intercept)),
pMem_post_pred = inv_logit(rnorm(n(), b_theta_intercept, sd_subj__theta_Intercept) +
rnorm(n(), b_theta_stimulation, sd_subj__theta_stimulation)),
pMem_ES_pred = pMem_post_pred - pMem_pre_pred
) %>%
select(-contains("b_"), -contains("sd_subj")) %>%
pivot_longer(-contains("."), names_to = c( "param", "stat"), names_pattern = "(.*)_(.*)", values_to = "value") %>%
pivot_wider(names_from = stat, values_from = value)group level posteriors
circSD_p1_wPrior <-
group_level_samples %>%
filter(str_detect(param, "circSD")) %>%
mutate(param = fct_relevel(param, c("prior_circSD_ES", "circSD_ES", "prior_circSD_pre", "circSD_pre", "prior_circSD_post", "circSD_post"))) %>%
ggplot() +
# posterior dist + interval for group mean
geom_halfeyeh(aes(y = param, x = mean), .width = c(.90, .95), position = position_nudge(y = 0.15)) +
# posterior predictive distribution for group means
stat_intervalh(aes(y = param, x = pred), .width = c(.5, .8, .95)) +
# posterior medians for each parameter estimate per subj
geom_point(data = circSD_subj_summary, aes(y = param, x = value), size = 2) +
# prior dist + interval for group mean
#geom_halfeyeh(data = group_level_prior_param_samples, aes(y = param, x = values), .width = c(.90, .95)) +
# decorations
scale_color_brewer() +
scale_x_continuous(breaks = pretty_breaks(10)) +
coord_cartesian(xlim=c(-50, 150)) +
labs(subtitle = "circSD: group level mean prior + posterior (median, 90%, 95% interval), \nsubject posterior medians, \ncondition predictive dist of subjects",
x = "circSD",
color = "interval")
# group level pMem pre, post and ES plot
pMem_p1_wPrior <-
group_level_samples %>%
filter(str_detect(param, "pMem")) %>%
mutate(param = fct_relevel(param, c("prior_pMem_ES", "pMem_ES", "prior_pMem_pre", "pMem_pre", "prior_pMem_post", "pMem_post"))) %>%
ggplot() +
# posterior dist + interval for group mean
geom_halfeyeh(aes(y = param, x = mean), .width = c(.90, .95), position = position_nudge(y = 0.15)) +
# posterior predictive distribution for group means
stat_intervalh(aes(y = param, x = pred), .width = c(.5, .8, .95)) +
# posterior medians for each parameter estimate per subj
geom_point(data = pMem_subj_summary, aes(y = param, x = value), size = 2) +
# decorations
scale_color_brewer() +
scale_x_continuous(breaks = pretty_breaks(10)) +
#coord_cartesian(xlim=c(-50, 150)) +
labs(subtitle = "pMem: group level mean prior + posterior (median, 90%, 95% interval), \nsubject posterior medians, \ncondition predictive dist of subjects",
x = "pMem",
color = "interval")
plot_grid(circSD_p1_wPrior, pMem_p1_wPrior, align = "hv", ncol = 1)
* Notes
Seems good in that there is consistent reduction in uncertainty from prior to posterior.
I should come up with a better plot to show the posterior estimates of group-level variance.
posterior predictive plot of errors
sim
conditions <- c(0,1)
nobs_per_cond_sim <- 1500
post_pred_fpath <- glue("{params$save_dir_str}/post_pred_obs.rds")
if (file.exists(post_pred_fpath)){
post_pred_sim <- readRDS(post_pred_fpath)
}else{
print("simulating")
posterior_arranged <-
spread_draws(model_fit, `(b|sd)_.*`, regex = TRUE) %>%
sample_n(2e3) %>%
mutate(sim_num = 1:n(),
nsubj = 1,
nobs_per_cond = nobs_per_cond_sim) %>%
select(-contains(".")) %>%
select(sim_num,
alpha0_mu = b_circSD_intercept,
alpha0_sigma = sd_subj__circSD_Intercept,
alphaD_mu = b_circSD_stimulation,
alphaD_sigma = sd_subj__circSD_stimulation,
beta0_mu = b_theta_intercept,
beta0_sigma = sd_subj__theta_Intercept,
betaD_mu = b_theta_stimulation,
betaD_sigma = sd_subj__theta_stimulation,
nsubj,
nobs_per_cond)
post_pred_sim <-
posterior_arranged %>%
mutate(
# use draw_subj to sample nsubj_sim per sim using group-level parameter draws
dataset = pmap(posterior_arranged, draw_subj),
stimulation = list(stimulation = rep(conditions, each = nobs_per_cond_sim))) %>%
# first unnest dataset, expanding by nsubj_sim and copying stimulation list to each subj
unnest(dataset) %>%
# then unnest stimulation, expanding by nobs_per_cond_sim*2
unnest(stimulation) %>%
# now use likelihood to simulation observations
mutate(
# evaluate and delink linear model on pMem
pMem = inv_logit(subj_beta0 + (subj_betaD * stimulation)),
# evaluate and delink linear model on circSD/kappa
k = sd2k_vec(
pracma::deg2rad(
exp(subj_alpha0 + (subj_alphaD * stimulation)))),
# use pMem to draw a 1 or 0 for each trial
memFlip = rbernoulli(n(), pMem),
# use k to draw from vonMises for each trial
vm_draw = rvonmises_vec(1, pi, k) - pi,
# draw from unif for each trial
unif_draw = runif(n(), -pi, pi),
# assign either vm_draw or unif_draw to each trial, depending on memFlip
obs_radian = memFlip * vm_draw + (1 - memFlip) * unif_draw,
# convert to degrees
obs_degree = obs_radian * (180/pi)
) %>%
select(-c(pMem, k, memFlip, vm_draw, unif_draw)) %>%
nest(subj_obs = c(stimulation, obs_degree, obs_radian)) %>%
nest(dataset = c(subj, subj_alpha0, subj_alphaD, subj_beta0, subj_betaD, nobs_per_condition, subj_obs))
saveRDS(post_pred_sim, post_pred_fpath)
}conditions <- c(0,1)
nobs_per_cond_sim <- 1500
post_predmean_fpath <- glue("{params$save_dir_str}/post_predmean_obs.rds")
if (file.exists(post_predmean_fpath)){
post_predmean_sim <- readRDS(post_predmean_fpath)
}else{
posterior_arranged <-
spread_draws(model_fit, `(b|sd)_.*`, regex = TRUE) %>%
sample_n(2e3) %>%
mutate(sim_num = 1:n(),
nobs_per_cond = nobs_per_cond_sim ) %>%
select(-contains(".")) %>%
select(sim_num,
subj_alpha0 = b_circSD_intercept,
subj_alphaD = b_circSD_stimulation,
subj_beta0 = b_theta_intercept,
subj_betaD = b_theta_stimulation,
nobs_per_cond)
post_predmean_sim <-
posterior_arranged %>%
# add stimulation covariates
mutate(
stimulation = list(stimulation = rep(conditions, each = nobs_per_cond_sim))
) %>%
# then unnest stimulation, expanding by nobs_per_cond_sim*2
unnest(stimulation) %>%
# now use likelihood to simulation observations
mutate(
# evaluate and delink linear model on pMem
pMem = inv_logit(subj_beta0 + (subj_betaD * stimulation)),
# evaluate and delink linear model on circSD/kappa
k = sd2k_vec(
pracma::deg2rad(
exp(subj_alpha0 + (subj_alphaD * stimulation)))),
# use pMem to draw a 1 or 0 for each trial
memFlip = rbernoulli(n(), pMem),
# use k to draw from vonMises for each trial
vm_draw = rvonmises_vec(1, pi, k) - pi,
# draw from unif for each trial
unif_draw = runif(n(), -pi, pi),
# assign either vm_draw or unif_draw to each trial, depending on memFlip
obs_radian = memFlip * vm_draw + (1 - memFlip) * unif_draw,
# convert to degrees
obs_degree = obs_radian * (180/pi)
) %>%
select(-c(pMem, k, memFlip, vm_draw, unif_draw)) %>%
nest(dataset = c(stimulation, obs_degree, obs_radian))
saveRDS(post_predmean_sim, post_predmean_fpath)
}posterior data prediction, w/ group-level variance
#######################################################
# calculate histogram quantile mats from each condition
sim_subj_obs_hist_count <- function(dataset, condition = 0){
dataset_obs <- dataset %>%
sample_n(1) %>%
unnest(subj_obs) %>%
filter(stimulation == condition) %>%
select(obs_degree)
breaks <- seq(-180, 180, 5)
bincount <- hist(dataset_obs$obs_degree, breaks = breaks, plot = FALSE)$counts
bincount_names <- glue("c{breaks[-1]}")
names(bincount) <- bincount_names
bincount_df <- data.frame(as.list(bincount))
return(bincount_df)
}
make_quantmat <- function(sim_datasets, condition = 0){
bincounts <- sim_datasets %>%
select(dataset) %>%
mutate(subj_hist_counts = map(dataset, sim_subj_obs_hist_count, condition)) %>%
select(-dataset) %>%
unnest(subj_hist_counts) %>%
as_tibble()
xvals <- seq(-177.5, 177.5, 5)
probs <- seq(0.1,0.9,0.1)
quantmat <- as.data.frame(matrix(NA, nrow=ncol(bincounts), ncol=length(probs)))
names(quantmat) <- paste0("p",probs)
quantmat <- cbind(quantmat, xvals)
for (iQuant in 1:length(probs)){
quantmat[,paste0("p",probs[iQuant])] <- as.numeric(summarise_all(bincounts, ~quantile(., probs[iQuant])))
}
return(quantmat)
}
quantmat_cond0 <- make_quantmat(post_pred_sim, 0)
quantmat_cond1 <- make_quantmat(post_pred_sim, 1)
#######################################################
# calculate ecdf quantile mats from each condition
# unnest post_pred_sim, using only 1 subj/dataset
unnested <-
post_pred_sim %>%
unnest(dataset) %>%
group_by(sim_num) %>%
sample_n(1) %>%
ungroup() %>%
unnest(subj_obs)
# calc quantiles mat for pre condition
ecdf_res_stim0 <-
unnested %>%
filter(stimulation == 0) %>%
group_by(sim_num) %>%
group_map(~ecdf(.$obs_degree )(seq(-180, 180, 1)))
stim0_ecdf_quantiles <- bind_cols(
tibble(x_val = seq(-180, 180, 1)),
as_tibble(colQuantiles(do.call(rbind, ecdf_res_stim0), probs = c(0.95, 0.5, 0.05 )))
)
# calc quantiles mat for post condition
ecdf_res_stim1 <-
unnested %>%
filter(stimulation == 1) %>%
group_by(sim_num) %>%
group_map(~ecdf(.$obs_degree )(seq(-180, 180, 1)))
stim1_ecdf_quantiles <- bind_cols(
tibble(x_val = seq(-180, 180, 1)),
as_tibble(colQuantiles(do.call(rbind, ecdf_res_stim1), probs = c(0.95, 0.5, 0.05 )))
)# blues
b_light <- "#8C9BC4"
b_light_highlight <- "#A0ADCE"
b_mid <- "#546BA9"
b_mid_highlight <- "#7385B8"
b_dark <- "#002381"
b_dark_highlight <- "#2E4B97"
#betancourt reds
r_light <- "#DCBCBC"
r_light_highlight <- "#C79999"
r_mid <- "#B97C7C"
r_mid_highlight <- "#A25050"
r_dark <- "#8F2727"
r_dark_highlight <- "#7C0000"
#######################################################
# plot histogram(density) per condition
ggplot(quantmat_cond0, aes(x = xvals)) +
geom_ribbon(aes(ymax = p0.9, ymin = p0.1), fill = r_light, alpha = 0.4) +
geom_line(aes(y = p0.5), color = r_dark, size = 1) +
geom_ribbon(data = quantmat_cond1, aes(ymax = p0.9, ymin = p0.1), fill = b_light, alpha = 0.4) +
geom_line(data = quantmat_cond1, aes(y = p0.5), color = b_dark, size = 1) +
scale_x_continuous(breaks=pretty_breaks(10)) +
labs(x = "error (degrees) [red = pre, blue = post]",
y = "count +/- quantile",
subtitle = glue("per-condition posterior pred dist (median line, 90% interval over {nrow(post_pred_sim)} sim datasets)\n({nobs_per_cond_sim} samples/cond, per subj-level draw, per group-level mean + sd draw)")) +
theme_cowplot()
#######################################################
# plot ecdf per condition
ggplot() +
geom_ribbon(data = stim0_ecdf_quantiles, aes(x = x_val, ymax = `95%`, ymin = `5%`), fill = "red", alpha = 0.3) +
geom_line(data = stim0_ecdf_quantiles, aes(x = x_val, y = `50%`), color = "red", size = 1) +
geom_ribbon(data = stim1_ecdf_quantiles, aes(x = x_val, ymax = `95%`, ymin = `5%`), fill = "blue", alpha = 0.3) +
geom_line(data = stim1_ecdf_quantiles, aes(x = x_val, y = `50%`), color = "blue", size = 1) +
scale_x_continuous(breaks=pretty_breaks(10)) +
geom_hline(yintercept = seq(0, 1, 0.25), linetype = "dashed", alpha = 0.2) +
labs(x = "error (degrees) [red = pre, blue = post]",
y = "cumulative prob.",
subtitle = glue("per-condition posterior pred cdf (median line, 90% interval over {nrow(post_pred_sim)} sim datasets) \n({nobs_per_cond_sim} samples/cond, per subj-level draw, per group-level mean + sd draw")) +
theme_cowplot()
posterior data prediction, w/o group-level variance
#######################################################
# calculate histogram quantile mats from each condition
sim_single_subj_obs_hist_count <- function(dataset, condition = 0){
dataset_obs <- dataset %>%
filter(stimulation == condition) %>%
select(obs_degree)
breaks <- seq(-180, 180, 5)
bincount <- hist(dataset_obs$obs_degree, breaks = breaks, plot = FALSE)$counts
bincount_names <- glue("c{breaks[-1]}")
names(bincount) <- bincount_names
bincount_df <- data.frame(as.list(bincount))
return(bincount_df)
}
make_quantmat <- function(sim_datasets, condition = 0){
bincounts <- sim_datasets %>%
select(dataset) %>%
mutate(subj_hist_counts = map(dataset, sim_single_subj_obs_hist_count, condition)) %>%
select(-dataset) %>%
unnest(subj_hist_counts) %>%
as_tibble()
xvals <- seq(-177.5, 177.5, 5)
probs <- seq(0.1,0.9,0.1)
quantmat <- as.data.frame(matrix(NA, nrow=ncol(bincounts), ncol=length(probs)))
names(quantmat) <- paste0("p",probs)
quantmat <- cbind(quantmat, xvals)
for (iQuant in 1:length(probs)){
quantmat[,paste0("p",probs[iQuant])] <- as.numeric(summarise_all(bincounts, ~quantile(., probs[iQuant])))
}
return(quantmat)
}
quantmat_cond0 <- make_quantmat(post_predmean_sim, 0)
quantmat_cond1 <- make_quantmat(post_predmean_sim, 1)
#######################################################
# calculate ecdf quantile mats from each condition
# unnest post_pred_sim, using only 1 subj/dataset
unnested <-
post_predmean_sim %>%
unnest(dataset)
# calc quantiles mat for pre condition
ecdf_res_stim0 <-
unnested %>%
filter(stimulation == 0) %>%
group_by(sim_num) %>%
group_map(~ecdf(.$obs_degree )(seq(-180, 180, 1)))
stim0_ecdf_quantiles <- bind_cols(
tibble(x_val = seq(-180, 180, 1)),
as_tibble(colQuantiles(do.call(rbind, ecdf_res_stim0), probs = c(0.95, 0.5, 0.05 )))
)
# calc quantiles mat for post condition
ecdf_res_stim1 <-
unnested %>%
filter(stimulation == 1) %>%
group_by(sim_num) %>%
group_map(~ecdf(.$obs_degree )(seq(-180, 180, 1)))
stim1_ecdf_quantiles <- bind_cols(
tibble(x_val = seq(-180, 180, 1)),
as_tibble(colQuantiles(do.call(rbind, ecdf_res_stim1), probs = c(0.95, 0.5, 0.05 )))
)# blues
b_light <- "#8C9BC4"
b_light_highlight <- "#A0ADCE"
b_mid <- "#546BA9"
b_mid_highlight <- "#7385B8"
b_dark <- "#002381"
b_dark_highlight <- "#2E4B97"
#betancourt reds
r_light <- "#DCBCBC"
r_light_highlight <- "#C79999"
r_mid <- "#B97C7C"
r_mid_highlight <- "#A25050"
r_dark <- "#8F2727"
r_dark_highlight <- "#7C0000"
#######################################################
# plot histogram(density) per condition
ggplot(quantmat_cond0, aes(x = xvals)) +
geom_ribbon(aes(ymax = p0.9, ymin = p0.1), fill = r_light, alpha = 0.4) +
geom_line(aes(y = p0.5), color = r_dark, size = 1) +
geom_ribbon(data = quantmat_cond1, aes(ymax = p0.9, ymin = p0.1), fill = b_light, alpha = 0.4) +
geom_line(data = quantmat_cond1, aes(y = p0.5), color = b_dark, size = 1) +
scale_x_continuous(breaks=pretty_breaks(10)) +
labs(x = "error (degrees) [red = pre, blue = post]",
y = "count +/- quantile",
subtitle = glue("per-condition posterior pred dist (median line, 90% interval over {nrow(post_predmean_sim)} sim datasets)\n({nobs_per_cond_sim} samples/cond, per subj-level draw, per group-level mean draw)")) +
theme_cowplot()
#######################################################
# plot ecdf per condition
ggplot() +
geom_ribbon(data = stim0_ecdf_quantiles, aes(x = x_val, ymax = `95%`, ymin = `5%`), fill = "red", alpha = 0.3) +
geom_line(data = stim0_ecdf_quantiles, aes(x = x_val, y = `50%`), color = "red", size = 1) +
geom_ribbon(data = stim1_ecdf_quantiles, aes(x = x_val, ymax = `95%`, ymin = `5%`), fill = "blue", alpha = 0.3) +
geom_line(data = stim1_ecdf_quantiles, aes(x = x_val, y = `50%`), color = "blue", size = 1) +
scale_x_continuous(breaks=pretty_breaks(10)) +
geom_hline(yintercept = seq(0, 1, 0.25), linetype = "dashed", alpha = 0.2) +
labs(x = "error (degrees) [red = pre, blue = post]",
y = "cumulative prob.",
subtitle = glue("per-condition posterior pred cdf (median line, 90% interval over {nrow(post_predmean_sim)} sim datasets) \n({nobs_per_cond_sim} samples/cond, per subj-level draw, per group-level mean draw")) +
theme_cowplot()
* Notes
Both the reduction in uncertainty and the hint of an effect are visible in the marginal subject plot and the average subject plot.